Question

The coefficient of x² in the expression (a + x)⁵ is 640. What is the value of a?​

Answer 1

Answer: a = cube root of 64

Step-by-step explanation:

Given below

Answer 2

Given :  The coefficient of x² in the expression (a + x)⁵ is 640.  

To find : the value of a?

Solution:

Term in a Binomial Expansion :  

 a binomial (a + b)ⁿ,

n is a positive integer,

( k + 1)th  term of that expansion

$^nC_{k}a^{n-k}b^k$

in (a + x)⁵  term containing x²

   ⁵C₂a³x²

 

   ⁵C₂a³ = 640

=> 10a³ = 640

=> a³ = 64

=> a = 4

Value of a = 4

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